Given a division problem with whole numbers, most students can easily describe
what the remainder means. However, when given a division problem in which the
divisor is a fraction or mixed number, attaching meaning to the remainder is not so easy.
In fact, many children (and adults) who correctly perform the paper-and-pencil
calculation, will incorrectly describe what the remainder means. Embedding division by
fractions and mixed numbers into real-world measurement problems can be very helpful
to learners who are struggling to make sense of these calculations.
Example 1: 23÷7 = 3, remainder 2
Children who have developed a part-whole concept of division, when asked what
the remainder means, will reply that there are 2 “things” left over. Or, they will say that
the remainder 2 means that each person will receive 3 wholes and 2
7 of whatever you are
dividing up and they will tend to name the things as cookies, cakes, etc. These answers
indicate that, even for problems presented without context, children tend to use context
when explaining remainders.
The two shorter lengths do not add up to more than the longest length. 3+3 is less than 9. Therefore, even if the two shorter lengths lay on top of the longer side, the two ends cannot meet to form a closed 3 sided figure
